What you see depends on where you are. In some countries there is basically no difference between what it takes to be eligible for amateur or pro events. In the US there is an extremely minor difference, so minor at the top levels that I don't even consider anyone who makes a US "Amateur" final to actually be an amateur.
A few years ago USA Dance (the governing body for IDSF-sanctioned or "amateur" competition in the US) tried to eliminate the term "amateur" and collapse professional and otherwise eligibility. That would have meant that job or earning status didn't matter, that everything depended on merit and proficiency. However, the membership didn't like that proposal and enough people voted against it that things were left as they are today. My personal opinion is that as painful as it would have been to change it, the levels would have worked themselves out over a short period (about two years, I guessed) and then we'd have a much simpler and clearer and more universally applicable system.
Anyway, to comply with International Olympic Committee rules that representatives to competitions like Worlds and the Olympics (even though dancesport isn't in the Olympics, it's an Olympic-recognized sport which means it has to play by Olympic rules if it wants a cance of getting in). This means that the US can no longer discriminate between amateurs and pros in the usual sense of the word. They have to let professionals compete in the selection events for the World Championships.
So, we're kind of at a halfway point in the US between what most people think of as "amateur" and what Don talks about as being a truly open system.